Apodized broadband partial reflectors

ABSTRACT

A broadband partial reflector includes a multilayer polymeric optical film having a total number of optical repeating units that monotonically increases in thickness value from a first side to a second side of the multilayer polymeric optical film. A baseline optical repeating unit thickness profile is defined by a first plurality of optical repeating units and having a first average slope, and a first apodized thickness profile of the multilayer polymeric optical film is defined by a second plurality of optical repeating units having a second average slope being at least 5 times greater than the first average slope. The second plurality of optical repeating units define the first side of the multilayer polymeric optical film and join the first plurality of optical repeating units. The second plurality of optical repeating units are in a range from 3-15% of the total number of optical repeating units.

FIELD

The present disclosure relates to, among other things, an optical filmconstruction that provides a smooth spectrum for the in-band transmittedand reflected light of broadband partial reflectors.

BACKGROUND

Multilayer optical films are known. Such films can incorporate a largenumber of thin layers of different light transmissive materials, thelayers being referred to as microlayers because they are thin enough sothat the reflection and transmission characteristics of the optical filmare determined in large part by constructive and destructiveinterference of light reflected from the layer interfaces. Depending onthe amount of birefringence (if any) exhibited by the individualmicrolayers, and the relative refractive index differences for adjacentmicrolayers, and also on other design characteristics, the multilayeroptical films can be made to have reflection and transmission propertiesthat may be characterized as a reflective polarizer in some cases, andas a mirror in other cases, for example.

Reflective polarizers composed of a plurality of microlayers whosein-plane refractive indices are selected to provide a substantialrefractive index mismatch between adjacent microlayers along an in-planeblock axis and a substantial refractive index match between adjacentmicrolayers along an in-plane pass axis, with a sufficient number oflayers to ensure high reflectivity for normally incident light polarizedalong one principal direction, referred to as the block axis, whilemaintaining low reflectivity and high transmission for normally incidentlight polarized along an orthogonal principal direction, referred to asthe pass axis, have been known for some time. See, e.g., U.S. Pat. No.3,610,729 (Rogers), U.S. Pat. No. 4,446,305 (Rogers et al.), and U.S.Pat. No. 5,486,949 (Schrenk et al.).

More recently, researchers from 3M Company have pointed out thesignificance of layer-to-layer refractive index characteristics of suchfilms along the direction perpendicular to the film, i.e. the z-axis,and shown how these characteristics play an important role in thereflectivity and transmission of the films at oblique angles ofincidence. See, e.g., U.S. Pat. No. 5,882,774 (Jonza et al.). Jonza etal. teach, among other things, how a z-axis mismatch in refractive indexbetween adjacent microlayers, more briefly termed the z-index mismatchor Δnz, can be tailored to allow the construction of multilayer stacksfor which the Brewster angle—the angle at which reflectance ofp-polarized light at an interface goes to zero—is very large or isnonexistent. This in turn allows for the construction of multilayermirrors and polarizers whose interfacial reflectivity for p-polarizedlight decreases slowly with increasing angle of incidence, or isindependent of angle of incidence, or increases with angle of incidenceaway from the normal direction. As a result, multilayer films havinghigh reflectivity for both s- and p-polarized light for any incidentdirection in the case of mirrors, and for the selected direction in thecase of polarizers, over a wide bandwidth, can be achieved.

Some multilayer optical films are designed for narrow band operation,i.e., over a narrow range of wavelengths, while others are designed foruse over a broad wavelength range such as substantially the entirevisible or photopic spectrum, or the visible or photopic wavelengthrange together with near infrared wavelengths, for example. Over theyears, designers and manufacturers of the latter type of films, i.e.,broadband multilayer optical films, have had to deal with the issue ofcolor. The color issue often arises when the film is intended for use ina visual display system, e.g., where the film is a broadband reflectivepolarizer or a broadband mirror, and the display system is a liquidcrystal display, luminaire, or backlight. A broadband reflectorgenerally includes a multilayer polymeric optical film having a totalnumber of optical repeating units that monotonically increases inthickness value from a first side to a second side of the multilayerpolymeric optical film. This arrangement of layer thicknesses isreferred to as a graded layer thickness profile. In such systems, it istypically undesirable for the film to impart a significant colored(non-white) appearance to the display, whether at normal incidence orfor obliquely incident light. The colored appearance occurs when thefilm has transmission or reflection characteristics that are not uniformover the visible portion of the spectrum. In the case of coextrudedpolymeric multilayer optical films, such non-uniformities are typicallythe result of imperfect control of the layer thickness profile of thefilm relative to a target profile. To avoid the color issue, polymericmultilayer optical films are often designed to provide along theirprincipal axes either extremely low reflectivity and high transmission(e.g. for a pass axis of a reflective polarizer that is viewed intransmission) or extremely high reflectivity and low transmission (e.g.for a block axis of a reflective polarizer, or for any in-plane axis ofa reflective mirror film that is viewed in reflected light).

Recently, broadband polymeric multilayer optical films have beenproposed that have intermediate amounts of reflectivity and transmissionfor light polarized parallel to at least one principal optic axis sothat some significant amount of incident light is reflected, and anothersignificant amount of the incident light (typically, the remainder ofthe incident light that is not reflected) is transmitted. Such films arereferred to herein as partially reflecting multilayer optical films, orpartially transmitting multilayer optical films. One approach toaddressing color issues in such films is to provide them with only asingle packet of microlayers with a carefully tailored layer thicknessprofile, and to manufacture them without the use of any layer multiplierdevices, to provide maximum control of the layer thickness profile and acorresponding minimum spectral variability in transmission or reflectionover the visible wavelength range. However even a carefully tailoredlayer thickness profile does not reduce color issues resulting fromin-band ringing.

BRIEF SUMMARY

The present disclosure describes apodized broadband reflectors thatexhibit reduced in-band spectral ringing, among other things.

In many embodiments, a broadband partial reflector is described. Thebroadband partial reflector includes a multilayer polymeric optical filmhaving a total number of optical repeating units that monotonicallyincreases in thickness value from a first side to a second side of themultilayer polymeric optical film. A baseline optical repeating unitthickness profile is defined by a first plurality of optical repeatingunits having a first average slope. A first apodized thickness profileof the multilayer polymeric optical film is defined by a secondplurality of optical repeating units and having a second average slopebeing at least 5 times greater than the first average slope. The secondplurality of optical repeating units define the first side of themultilayer polymeric optical film and join the first plurality ofoptical repeating units. The second plurality of optical repeating unitsare in a range from 3% to 15% or from 5% to 10% of the total number ofoptical repeating units. In some embodiments, a broadband partialreflector includes a second apodized thickness profile and is describedherein. This broadband partial reflector is similar to the embodimentdescribed above and further includes a second apodized thickness profileof the multilayer polymeric optical film defined by a third plurality ofoptical repeating units having a third average slope being at least 5times greater than the first average slope. The third plurality ofoptical repeating units define the second side of the multilayerpolymeric optical film and join the first plurality of optical repeatingunits. The third plurality of optical repeating units are in a rangefrom 5-10% or from 3-15% of the total number of optical repeating units.

The optical film (e.g., broadband partial reflector), and film articlesdescribed herein may provide one or more advantages over prior opticalfilms or film articles. For example, prior broadband partial reflectorswere susceptible to in-band ringing, while the broadband partialreflectors described herein substantially eliminate in-band ringing.Accordingly, the broadband partial reflectors described herein provide asmoother spectrum for the in-band transmitted and reflected light. Theseand other advantages of the various embodiments of the devices andmethods described herein will be readily apparent to those of skill inthe art upon reading the disclosure presented herein.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure may be more completely understood in consideration of thefollowing detailed description of various embodiments of the disclosurein connection with the accompanying drawings, in which:

FIG. 1 is a schematic perspective view of an exemplary optical repeatunit (ORU) of a multilayer optical film;

FIG. 2 is a schematic perspective view of a portion of a multilayeroptical film, this view showing a packet of microlayers and a pluralityof ORUs;

FIG. 3 is a schematic perspective view of a reflective polarizing film;

FIG. 4 is a schematic cross-sectional view of a broadband partialreflector;

FIG. 5 is a graph of a baseline thickness profile and an apodizedthickness profile that can be used to fabricate a broadband reflector ofExample 1;

FIG. 6 is a graph of spectra modeled for a broadband reflector ofExample 1 having a baseline layer thickness profile;

FIG. 7 is a graph of spectra modeled for a broadband reflector ofExample 1 having an apodized baseline layer thickness profile;

FIG. 8 is a graph of spectra modeled for a broadband reflector ofExample 1 having an apodized baseline layer thickness profile with andwithout optically thick layers;

FIG. 9 is a graph of a baseline thickness profile and an apodizedthickness profile that can be used to fabricate a broadband reflectorwith a high spectral slope;

FIG. 10 is a graph of spectra modeled for a broadband reflectordescribed in FIG. 9;

FIG. 11 is a magnified view of layer profile graph shown in FIG. 5 curve5 b;

FIG. 12 is a graph of an apodized thickness profile for a firstpolymeric film;

FIG. 13 is a graph of spectra measured for a broadband reflectordescribed in FIG. 12;

FIG. 14 is a graph of an apodized thickness profile for a secondpolymeric film;

FIG. 15 is a graph of spectra measured for a broadband reflectordescribed in FIG. 14;

FIG. 16 is a graph of an apodized thickness profile for a thirdpolymeric film; and

FIG. 17 is a graph of spectra measured for a broadband reflectordescribed in FIG. 16.

The schematic drawings presented herein are not necessarily to scale.Like numbers used in the figures refer to like components, steps and thelike. However, it will be understood that the use of a number to referto a component in a given figure is not intended to limit the componentin another figure labeled with the same number. In addition, the use ofdifferent numbers to refer to components is not intended to indicatethat the different numbered components cannot be the same or similar.

DETAILED DESCRIPTION

In the following detailed description, reference is made to theaccompanying drawings that form a part hereof, and in which are shown byway of illustration several specific embodiments of devices, systems andmethods. It is to be understood that other embodiments are contemplatedand may be made without departing from the scope or spirit of thepresent disclosure. The following detailed description, therefore, isnot to be taken in a limiting sense.

All scientific and technical terms used herein have meanings commonlyused in the art unless otherwise specified. The definitions providedherein are to facilitate understanding of certain terms used frequentlyherein and are not meant to limit the scope of the present disclosure.

As used in this specification and the appended claims, the singularforms “a”, “an”, and “the” encompass embodiments having pluralreferents, unless the content clearly dictates otherwise.

As used in this specification and the appended claims, the term “or” isgenerally employed in its sense including “and/or” unless the contentclearly dictates otherwise.

As used herein, “have”, “having”, “include”, “including”, “comprise”,“comprising” or the like are used in their open ended sense, andgenerally mean “including, but not limited to.” It will be understoodthat the terms “consisting of” and “consisting essentially of” aresubsumed in the term “comprising,” and the like.

Any direction referred to herein, such as “top,” “bottom,” “left,”“right,” “upper,” “lower,” “above,” below,” and other directions andorientations are described herein for clarity in reference to thefigures and are not to be limiting of an actual device or system or useof the device or system. Many of the devices, articles or systemsdescribed herein may be used in a number of directions and orientations.

The present disclosure describes, among other things, an optical filmconstruction that provides a smooth spectrum for the in-band transmittedand reflected light of broadband partial reflectors. As describedherein, the broadband partial reflectors described herein substantiallyeliminate in-band ringing. Accordingly, the broadband partial reflectorsdescribed herein provide a smooth spectrum for the in-band transmittedand reflected light. It has been found that broadband partial reflectoroptical film that has apodized graded thickness profile reduces orsubstantially eliminates in-band spectrum ringing and consequentiallyreduces or substantially eliminates undesired color. The term“apodization,” sometimes referred to as “tapering,” is derived from aclass of mathematical techniques that generally are applied in thefields of signal processing, electromagnetics and optics. When physicalstructures interact with electromagnetic fields, such as a polymericmultilayer optical film interacting with infrared, visible, and/orultraviolet light, spectral features will generally occur that are theresult of the discontinuities associated with the terminations of agraded, resonant layer profile. For the present disclosure, we use theterm apodization to describe a technique to terminate a graded layerthickness profile so as to minimize undesirable spectral features suchas spectral ringing.

The broadband partial reflectors described herein may be used for anysuitable purpose, including but not limited to optical displays, opticalgraphics or the like. While the present disclosure is not so limited, anappreciation of various aspects of the disclosure will be gained througha discussion of the examples provided below.

As mentioned above, one challenge faced by designers and manufacturersof polymeric multilayer optical films that are intended to be both (1)partially reflecting along a principal axis at normal and oblique anglesand (2) broadband (i.e., intended to provide partial reflectivity over abroad wavelength range) is unintended and undesired color. Suchundesired color is can be manifested as relatively high frequencyvariability in the optical transmission and reflection spectra. Forpurposes of the figures illustrated and described herein, forsimplicity, the multilayer optical film bodies are assumed to have nospatial variability in the plane of the film body. Thus, the spectralreflection and transmission characteristics of a given film body areassumed to be independent of the position or location on the film (e.g.,the (x,y) coordinate) at which they are measured.

Referring now to FIG. 1, a schematic perspective view of an exemplaryoptical repeat unit (ORU) of a multilayer optical film is illustrated.FIG. 1 depicts only two layers of a multilayer optical film 100, whichcan include tens or hundreds of such layers arranged in one or morecontiguous packets or stacks. The film 100 includes individualmicrolayers 102, 104, where “microlayers” refer to layers that aresufficiently thin so that light reflected at a plurality of interfacesbetween such layers undergoes constructive or destructive interferenceto give the multilayer optical film the desired reflective ortransmissive properties. The microlayers 102, 104 can together representone optical repeat unit (ORU) of the multilayer stack, an ORU being thesmallest set of layers that recur in a repeating pattern throughout thethickness of the stack. The microlayers have different refractive indexcharacteristics so that some light is reflected at interfaces betweenadjacent microlayers. For optical films designed to reflect light atultraviolet, visible, or near-infrared wavelengths, each microlayertypically has an optical thickness (i.e., a physical thicknessmultiplied by refractive index) of less than about 1 micrometer. Thickerlayers can, however, also be included, such as skin layers at the outersurfaces of the film, or protective boundary layers (PBL) disposedwithin the film that separate packets of microlayers, as desired.

Refractive indices of one of the microlayers (e.g. layer 102 of FIG. 1,or the “A” layers of FIG. 2 below) for light polarized along principalx-, y-, and z-axes are n1x, n1y, and n1z, respectively. The mutuallyorthogonal x-, y-, and z-axes can, for example, correspond to theprincipal directions of the dielectric tensor of the material. In manyembodiments, and for discussion purposes, the principle directions ofthe different materials are coincident, but this need not be the case ingeneral. The refractive indices of the adjacent microlayer (e.g. layer104 in FIG. 1, or the “B” layers in FIG. 2) along the same axes are n2x,n2y, n2z, respectively. The differences in refractive index betweenthese layers are Δnx (=n1x−n2x) along the x-direction, Δny (=n1y−n2y)along the y-direction, and Δnz (=n1z−n2z) along the z-direction. Thenature of these refractive index differences, in combination with thenumber of microlayers in the film (or in a given stack of the film) andtheir thickness distribution, controls the reflective and transmissivecharacteristics of the film (or of the given stack of the film). Forexample, if adjacent microlayers have a large refractive index mismatchalong one in-plane direction (Δnx large) and a small refractive indexmismatch along the orthogonal in-plane direction (Δny≈0), the film orpacket may behave as a reflective polarizer for normally incident light.A reflective polarizer may be considered to be an optical body thatstrongly reflects normally incident light that is polarized along onein-plane axis, referred to as the “block axis”, if the wavelength iswithin the reflection band of the packet, and strongly transmits suchlight that is polarized along an orthogonal in-plane axis, referred toas the “pass axis”.

If desired, the refractive index difference (Δnz) between adjacentmicrolayers for light polarized along the z-axis can also be tailored toachieve desirable reflectivity properties for the p-polarizationcomponent of obliquely incident light. To maintain near on-axisreflectivity of p-polarized light at oblique angles of incidence, thez-index mismatch Δnz between microlayers can be controlled to besubstantially less than the maximum in-plane refractive index differenceΔnx, such that Δnz≦0.5*Δnx. Alternatively, Δnz≦0.25*Δnx. A zero or nearzero magnitude z-index mismatch yields interfaces between microlayerswhose reflectivity for p-polarized light is constant or near constant asa function of incidence angle. Furthermore, the z-index mismatch Δnz canbe controlled to have the opposite polarity compared to the in-planeindex difference Δnx, i.e., Δnz<0. This condition yields interfaceswhose reflectivity for p-polarized light increases with increasingangles of incidence, as is the case for s-polarized light. If Δnz>0,then the reflectivity for p-polarized light decreases with angle ofincidence. The foregoing relationships also of course apply torelationships involving Δnz and Δny, e.g., in cases where significantreflectivity and transmission are desired along two principal in-planeaxes (such as a balanced or symmetric partially reflecting mirror film,or a partial polarizing film whose pass axis has significantreflectivity at normal incidence).

In the schematic side view of FIG. 2, more interior layers of amultilayer film 110 are shown so that multiple ORUs can be seen. Thefilm is shown in relation to a local x-y-z Cartesian coordinate system,where the film extends parallel to the x- and y-axes, and the z-axis isperpendicular to the film and its constituent layers and parallel to athickness axis of the film.

In FIG. 2, the microlayers are labeled “A” or “B”, the “A” layers beingcomposed of one material and the “B” layers being composed of adifferent material, these layers being stacked in an alternatingarrangement to form optical repeat units or unit cells ORU 1, ORU 2, . .. ORU 6 as shown. In many embodiments, a multilayer optical filmcomposed entirely of polymeric materials would include many more than 6optical repeat units if high reflectivities are desired. The multilayeroptical film 110 is shown as having a substantially thicker layer 112,which may represent an outer skin layer, or a protective boundary layer(“PBL”, see U.S. Pat. No. 6,783,349 (Neavin et al.)) that separates thestack of microlayers shown in the figure from another stack or packet ofmicrolayers (not shown). If desired, two or more separate multilayeroptical films can be laminated together, e.g. with one or more thickadhesive layers, or using pressure, heat, or other methods to form alaminate or composite film.

In some cases, the microlayers can have thicknesses and refractive indexvalues corresponding to a ¼-wave stack, i.e., arranged in ORUs eachhaving two adjacent microlayers of equal optical thickness (f-ratio=50%,the f-ratio being the ratio of the optical thickness of a constituentlayer “A” to the optical thickness of the complete optical repeat unit),such ORU being effective to reflect by constructive interference lightwhose wavelength λ is twice the overall optical thickness of the opticalrepeat unit, where the “optical thickness” of a body refers to itsphysical thickness multiplied by its refractive index. In other cases,the optical thickness of the microlayers in an optical repeat unit maybe different from each other, whereby the f-ratio is greater than orless than 50%. For purposes of the present application, we contemplatemultilayer optical films whose f-ratio may be any suitable value, and donot limit ourselves to films whose f-ratio of 50%. Accordingly, in theembodiment of FIG. 2, the “A” layers are depicted for generality asbeing thinner than the “B” layers. Each depicted optical repeat unit(ORU 1, ORU 2, etc.) has an optical thickness (OT1, OT2, etc.) equal tothe sum of the optical thicknesses of its constituent “A” and “B” layer,and each optical repeat unit reflects light whose wavelength λ is twiceits overall optical thickness. In exemplary embodiments, the opticalthicknesses of the ORUs differ according to a thickness gradient alongthe z-axis or thickness direction of the film, whereby the opticalthickness of the optical repeat units increases, decreases, or followssome other functional relationship as one progresses from one side ofthe stack (e.g. the top) to the other side of the stack (e.g. thebottom). Such thickness gradients can be used to provide a widenedreflection band to provide substantially spectrally flat transmissionand reflection of light over the extended wavelength band of interest,and also over all angles of interest. Alternatively, the layer thicknessgradient of the disclosed packets of microlayers may be deliberatelytailored to provide reflection and transmission spectra that changesignificantly over the wavelength range of interest. For example, it maybe desirable for the multilayer optical film body to transmit (orreflect) more blue light than red light, or vice versa, or to transmit(or reflect) more green light than blue light and red light. Althoughsuch desired spectral non-uniformities may cause the multilayer opticalfilm body to exhibit a colored (non-clear or non-neutral) appearance,this desired color is often distinguishable from the undesired colordiscussed elsewhere herein in that the desired color is associated withrelatively slow changes in the spectral reflection or transmission,whereas the undesired color is associated with faster changes in thoseparameters as a function of wavelength. For example, spectralnon-uniformities in reflection or transmission associated with desiredcolor may vary as a function of wavelength with characteristic periodsof about 100 nm or greater, whereas spectral non-uniformities inreflection or transmission associated with undesired color may vary as afunction of wavelength with characteristic periods of less than about 50nm, although this number depends somewhat on the magnitude of localizeddisruptions in the layer thickness profile.

To achieve reflectivity with a reasonable number of layers, adjacentmicrolayers may exhibit a difference in refractive index (Δnx) for lightpolarized along the x-axis of at least 0.03, for example. If highreflectivity is desired for two orthogonal polarizations, then theadjacent microlayers also may exhibit a difference in refractive index(Δny) for light polarized along the y-axis of at least 0.03, forexample. In some cases, adjacent microlayers may have refractive indexmismatches along the two principal in-plane axes (Δnx and Δny) that areclose in magnitude, in which case the film or packet may behave as anon-axis mirror or partial mirror. Alternatively, for reflectivepolarizers that are designed to be partially reflective for the passaxis polarization, adjacent microlayers may exhibit a large differencein refractive index (Δnx) for light polarized along the x-axis and asmaller but still substantial difference in refractive index (Δny) forlight polarized along the y-axis. In variations of such embodiments, theadjacent microlayers may exhibit a refractive index match or mismatchalong the z-axis (Δnz=0 or Δnz large), and the mismatch may be of thesame or opposite polarity or sign as the in-plane refractive indexmismatch(es). Such tailoring of Δnz plays a key role in whether thereflectivity of the p-polarized component of obliquely incident lightincreases, decreases, or remains the same with increasing incidenceangle.

Although the examples herein describe reflectors whose reflectivityincreases with angle of incidence, partial reflectors whose reflectivityalong a given principal axis decreases with angle of incidence can bemade with reduced color using the same techniques described herein. Thisis particularly important for films whose reflectivity is large atnormal incidence and are viewed in transmitted light at various angles,including normal incidence.

At least some of the microlayers in at least one packet of the disclosedmultilayer optical films may if desired be birefringent, e.g.,uniaxially birefringent or biaxially birefringent, although in someembodiments, microlayers that are all isotropic may also be used. Insome cases, each ORU may include one birefringent microlayer, and asecond microlayer that is either isotropic or that has a small amount ofbirefringence relative to the other microlayer. In alternative cases,each ORU may include two birefringent microlayers.

Exemplary multilayer optical films are composed of polymer materials andmay be fabricated using coextruding, casting, and orienting processes.Reference is made to U.S. Pat. No. 5,882,774 (Jonza et al.) “OpticalFilm”, U.S. Pat. No. 6,179,949 (Merrill et al.) “Optical Film andProcess for Manufacture Thereof”, U.S. Pat. No. 6,783,349 (Neavin etal.) “Apparatus for Making Multilayer Optical Films”, and U.S. PatentApplication 61/332,401 entitled “Feedblock for Manufacturing MultilayerPolymeric Films”, filed May 7, 2010. The multilayer optical film may beformed by coextrusion of the polymers as described in any of theaforementioned references. The polymers of the various layers may bechosen to have similar rheological properties, e.g., melt viscosities,so that they can be co-extruded without significant flow disturbances.Extrusion conditions are chosen to adequately feed, melt, mix, and pumpthe respective polymers as feed streams or melt streams in a continuousand stable manner. Temperatures used to form and maintain each of themelt streams may be chosen to be within a range that avoids freezing,crystallization, or unduly high pressure drops at the low end of thetemperature range, and that avoids material degradation at the high endof the range.

In brief summary, the fabrication method can include: (a) providing atleast a first and a second stream of resin corresponding to the firstand second polymers to be used in the finished film; (b) dividing thefirst and the second streams into a plurality of layers using a suitablefeedblock, such as one that includes: (i) a gradient plate comprisingfirst and second flow channels, where the first channel has across-sectional area that changes from a first position to a secondposition along the flow channel, (ii) a feeder tube plate having a firstplurality of conduits in fluid communication with the first flow channeland a second plurality of conduits in fluid communication with thesecond flow channel, each conduit feeding its own respective slot die,each conduit having a first end and a second end, the first end of theconduits being in fluid communication with the flow channels, and thesecond end of the conduits being in fluid communication with the slotdie, and (iii) optionally, an axial rod heater located proximal to saidconduits; (c) passing the composite stream through an extrusion die toform a multilayer web in which each layer is generally parallel to themajor surface of adjacent layers; and (d) casting the multilayer webonto a chill roll, sometimes referred to as a casting wheel or castingdrum, to form a cast multilayer film. This cast film may have the samenumber of layers as the finished film, but the layers of the cast filmare typically much thicker than those of the finished film. Furthermore,the layers of the cast film are typically all isotropic. A multilayeroptical film with controlled low frequency variations in reflectivityand transmission over a wide wavelength range can be achieved by thethermal zone control of the axial rod heater, see e.g. U.S. Pat. No.6,783,349 (Neavin et al.).

In some cases, the fabrication equipment may employ one or more layermultipliers to multiply the number of layers in the finished film. Inother embodiments, the films can be manufactured without the use of anylayer multipliers. Although layer multipliers greatly simplify thegeneration of a large number of optical layers, they may impartdistortions to each resultant packet of layers that are not identicalfor each packet. For this reason, any adjustment in the layer thicknessprofile of the layers generated in the feedblock is not the same foreach packet, i.e., all packets cannot be simultaneously optimized toproduce a uniform smooth spectrum free of spectral disruptions. Thus, anoptimum profile, for low transmitted and reflected color, can bedifficult to make using multi-packet films manufactured usingmultipliers. If the number of layers in a single packet generateddirectly in a feedblock do not provide sufficient reflectivity, then twoor more such films can be attached to increase the reflectivity. Furtherdiscussion of layer thickness control, so as to provide smooth spectralreflectivity and transmission for low color films, is provided in PCTpublication WO 2008/144656 (Weber et al.).

If the optical thicknesses of all of the microlayers in a givenmultilayer film were designed to be the same, the film would providehigh reflectivity over only a narrow band of wavelengths. Such a filmwould appear highly colored if the band were located somewhere in thevisible spectrum, and the color would change as a function of angle. Inthe context of display and lighting applications, films that exhibitnoticeable colors are generally avoided, although in some cases it maybe beneficial for a given optical film to introduce a small amount ofcolor to correct for color imbalances elsewhere in the system. Exemplarymultilayer optical film bodies are provided with broad band reflectivityand transmission, e.g. over the entire visible spectrum, by tailoringthe microlayers—or more precisely, the optical repeat units (ORUs),which in many (but not all) embodiments correspond to pairs of adjacentmicrolayers—to have a range of optical thicknesses. Typically, themicrolayers are arranged along the z-axis or thickness direction of thefilm from a thinnest ORU on one side of the film or packet to a thickestORU on the other side, with the thinnest ORU reflecting the shortestwavelengths in the reflection band and the thickest ORU reflecting thelongest wavelengths.

After the multilayer web is cooled on the chill roll, it can be drawn orstretched to produce a finished or near-finished multilayer opticalfilm. The drawing or stretching accomplishes two goals: it thins thelayers to their desired final thicknesses, and it may orient the layerssuch that at least some of the layers become birefringent. Theorientation or stretching can be accomplished along the cross-webdirection (e.g. via a tenter), along the down-web direction (e.g. via alength orienter), or any combination thereof, whether simultaneously orsequentially. If stretched along only one direction, the stretch can be“unconstrained” (wherein the film is allowed to dimensionally relax inthe in-plane direction perpendicular to the stretch direction) or“constrained” (wherein the film is constrained and thus not allowed todimensionally relax in the in-plane direction perpendicular to thestretch direction). If stretched along both in-plane directions, thestretch can be symmetric, i.e., equal along the orthogonal in-planedirections, or asymmetric. Alternatively, the film may be stretched in abatch process. In any case, subsequent or concurrent draw reduction,stress or strain equilibration, heat setting, and other processingoperations can also be applied to the film.

In reference to traditional polarizing films, light can be considered tobe polarized in two orthogonal planes, where the electric vector of thelight, which is transverse to the propagation of the light, lies withina particular plane of polarization. In turn, the polarization state of agiven light ray can be resolved into two different polarization states:p-polarized and s-polarized light. P-pol light is polarized in the planeof incidence of the light ray and a given surface, where the plane ofincidence is a plane containing both the local surface normal vector andthe light ray propagation direction or vector.

FIG. 3 is a schematic perspective view of a reflective polarizing film.FIG. 3 illustrates a light ray 130 that is incident on a polarizer 110at an angle of incidence θ, thereby forming a plane of incidence 132.The polarizer 110 includes a pass axis 114 that is parallel to they-axis, and a block axis 116 that is parallel to the x-axis. The planeof incidence 132 of ray 130 is parallel to the block axis 116. Ray 130has a p-polarized component that is in the plane of incidence 132, andan s-polarized component that is orthogonal to the plane of incidence132. The p-pol light of ray 130 will be substantially reflected by thepolarizer, while the s-pol light of ray 130 is, at least in part,transmitted.

Further, FIG. 3 illustrates ray 120 that is incident on polarizer 100 ina plane of incidence 122 that is parallel to the pass axis 114 of thepolarizer 110. As a result, assuming that the polarizer 110 is a perfectpolarizer that has a reflectance of 100% at all angles of incident lightfor light polarized in the block axis and 0% at all angles of incidentlight for light polarized in the pass axis, the polarizer transmitss-pol light of ray 130 and the p-pol light of ray 120, while reflectingthe p-pol light of ray 130 and the s-pol light of ray 120. In otherwords, the polarizer 110 will transmit a combination of p- and s-pollight. The amount of transmission and reflection of p- and s-pol lightwill depend on the characteristics of the polarizer as is furtherdescribed herein.

FIG. 4 is a schematic cross-sectional view of a broadband partialreflector 200. A broadband partial reflector 200 includes a multilayerpolymeric optical film 200 having a total number of optical repeatingunits that monotonically increases in thickness value from a first side201 to a second side 202 of the multilayer polymeric optical film 200.In many embodiments, the total number of optical repeating units is in arange from 50 to 1000. In many embodiments, the broadband partialreflector 200 reflects 10-90% of visible or IR light over a band of atleast 100 nm width or over a band of at least 200 nm width or over aband of at least 300 nm width.

A baseline optical repeating unit thickness profile defined by a firstplurality of optical repeating units 210 and having a first averageslope. The first plurality of optical repeating units 210 are definedbetween a first layer 211 and a final layer 212.

A first apodized thickness profile of the multilayer polymeric opticalfilm defined by a second plurality of optical repeating units 220 andhaving a second average slope being at least 5 times greater than thefirst average slope. In many embodiments, the second average slope is atleast 10 times greater than the first average slope. The secondplurality of optical repeating units 220 define the first side 201 ofthe multilayer polymeric optical film and join the first plurality ofoptical repeating units 210. The second plurality of optical repeatingunits 220 are in a range from 5-10% or 3-15% of the total number ofoptical repeating units, or may contain from 4 to 20 optical repeatingunits. The second plurality of optical repeating units 220 are definedbetween a first layer 221 and a final layer 222. The final layer 222 ofthe second plurality of optical repeating units 220 is adjacent to andin contact with the first layer 211 of the first plurality of opticalrepeating units 210.

In many embodiments the broadband partial reflector 200 includes asecond apodized thickness profile. The second apodized thickness profileof the multilayer polymeric optical film 200 is defined by a thirdplurality of optical repeating units 230 and has a third average slopebeing at least 5 times greater than the first average slope. In manyembodiments, the third average slope is at least 10 times greater thanthe first average slope. The third plurality of optical repeating units230 define the second side 202 of the multilayer polymeric optical film200 and join the first plurality of optical repeating units 210. Thethird plurality of optical repeating units 230 are in a range from 5-10%or 3-15% of the total number of optical repeating units, or may containfrom 4 to 20 optical repeating units. The third plurality of opticalrepeating units 230 are defined between a first layer 231 and a finallayer 232. The first layer 231 of the third plurality of opticalrepeating units 230 is adjacent to and in contact with the final layer212 of the first plurality of optical repeating units 210.

In many embodiments, the second plurality of optical repeating units 220(i.e., first apodized thickness profile) increase in thickness from thefirst layer 221 and a final layer 222 in a range from 1.1× to 2×. Inmany embodiments, the third plurality of optical repeating units 230(i.e., second apodized thickness profile) increase in thickness from thefirst layer 231 and a final layer 232 in a range from 1.2× to 2× (seeFIG. 5 open circles). In many embodiments, the first apodized thicknessprofile exponentially deviates from the baseline optical repeating unitthickness profile. In many embodiments, the second apodized thicknessprofile exponentially deviates from the baseline optical repeating unitthickness profile. The first apodized thickness profile can have a firstlayer 221 thickness that is at least 15% thinner or at least 25% thinnerthan any of the first plurality of optical repeating units 210. Thesecond apodized thickness profile has a final layer thickness 232 thatis at least 15% thicker or at least 25% thicker than any of the firstplurality of optical repeating units 210. In many embodiments, thebroadband partial reflector 200 includes an optically thick layer (seeFIG. 2 element 112) that is optically coupled to the first side 201 orsecond side 202. The optically thick layer is at least 10× thicker thanat least one of the first plurality of optical repeating units 210. Insome embodiments the broadband partial reflector 200 includes anantireflection layer disposed on the first side 201 and/or the secondside 202.

At least one difference between vacuum deposited stack designs andcoextruded polymeric multilayer stack designs is the shape of the layerprofile distribution. With vacuum deposited films, the desired spectrumis achieved by individually adjusting the thickness of every layer inthe stack so it conforms to a computer optimized stack design. In thismanner, issues such as spectral ripple are routinely minimized. Adjacentlayers sometimes differ in thickness by a factor of 10, with thicknessvalues often ranging from about 0.05λ, to 1.0λ. With coextrudedpolymeric film stacks, on-line monitoring and control of individuallayers in this manner is not yet a viable option with this technology.As a result, spectral shape is controlled mainly by the shape of acontinuous and smoothly varying layer thickness profile, such as profile5A in FIG. 5. Such profiles are not restricted to polymeric film stacks,and the apodizing profiles disclosed herein can be applied to any stackthat utilizes layer thickness profiles that are graded from thin tothick layers in a substantially monotonic fashion.

One should also note that the classic examples of apodized stacks arenot broadband reflectors but are stacks that are centered, i.e. tuned,for one (i.e., a single) wavelength. In such a stack, all opticalrepeating units have substantially the same thickness value. For thosestacks, there is no “in-band” ripple, only side-band ripple.Furthermore, the apodization profile for those stacks generally extendsthrough much or sometimes all of the layers of the stack and typicallyuse profiles of index change, not profiles of thickness change. Commonexamples can be found in the fiber optic industry where the “stack” is amodulated index profile along the length of the fiber. Some apodizationprofiles are Cosine, Guassian, Quintic, Septic or Sinc function indexprofiles, for example.

By broadband reflectors we mean reflectors for which the longest andshortest wavelength in the reflection band have a wavelength ratio ofabout 2:1 or more, although generally they can be as low as 1.5:1 and upto as large as 5:1 for polymeric reflectors. In the following,non-limiting examples are presented, which describe various embodimentsof the articles and methods discussed above.

EXAMPLES Example 1 Computer Modeled Layer Profiles and Spectra

FIG. 5 presents two distinctly different layer thickness profiles thatcan be used to fabricate a broadband reflector: a baseline design for abroadband reflector, and an apodized version. The apodized version showsthe end sections of a baseline profile replaced with an apodizingprofile (curve 5 b) which terminates with a high positive slope. Thebaseline profile (curve 5 a) was based on a simple power law profile foreach layer n, from n=1 to N, where the thickness t of each layer isgiven by t=T₀*(1.005)^n where T₀ is a constant scaling factor and n isthe layer number. The baseline profile shown here is modified with asmall adjustment that slightly increases the curvature to help adjustfor index dispersion. Spectra were generated for profiles such as theseusing optics computer models known to those skilled in the art.According to the modeling results, the baseline layer thickness profile(curve 5 a) yielded the pass spectrum 6 a and block spectrum 6 b, asshown in FIG. 6. The apodized baseline layer thickness profile (curve 5b) yielded the pass spectrum 7 a and block spectrum 7 b, as shown inFIG. 7. Notice that the in-band spectral ringing of FIG. 6 is reduced inFIG. 7 due to the apodizing profile (curve 5 b).

The layer thickness values shown in FIG. 5 are equal to ½ of thephysical thickness of the optical repeating units. The modeling wasperformed using ¼ wave optical thickness for each layer, meaning thephysical thickness values were adjusted for the differing index valuesof the high and low index materials.

The modeled spectra of FIG. 6 were both modeled for a birefringent filmstack which has the following indices of refraction: high index layersnx1=1.791, ny=1.675, nz=1.490, and low index layers nx2=ny2=nz2=1.564.This stack also included 20 micrometer thick skin layers of the lowindex material. This birefringent layer index set can be achieved withan asymmetrical orientation of a coPEN copolymer (90% PEN, 10% PET). Thelow index layers are formed from PETg GN071 which is available fromEastman Chemicals, Kingsport, Tenn. Note the in-band ringing of thespectra, especially for the pass axis spectra (curve 6 a). As thereflectivity approaches 100% for the block axis (curve 6 b), theoscillations on this plotted scale appear to be much smaller, but on aLog scale are still quite large. Most reflectors that have reflectancemagnitudes near 99% are rarely used in transmission though, and may havelittle need for apodization, but this technique can be used onreflectors having any value of reflectivity.

In order to reduce the spectral oscillations, the profile of FIG. 5 wasexplored, with unexpected and significant success. The “apodized”profile (curve 5 b) yielded the spectra of FIG. 7 which exhibit asignificant reduction in spectral ringing. This apodized profile wasobtained by adding an exponential tail to each end of the base profile.The exponential thickness profile was given by t=A*Exp(−n/d) where n isthe layer number (from a given end), A is a fractional amplitude and dis a scalar (the 1/e value) that is a measure of how far the apodizationprofile extends into the stack. These values were added to the baselinelayer values. A₁ for the apodized profile on the thin layer end was −0.3and A₂₇₅ for the thick layer end was +0.25. In other words, layer 1 ofthe apodized profile was 30% thinner than layer 1 of the originalbaseline profile for layer 1 and layer 275 is 25% thicker than layer 275of the original profile. Several variations (not shown) on theapodization shown in FIG. 5 were explored. Similar apodizationamplitudes on either end of the stack appeared to provide similarreduction of ringing on the respective ends of the spectrum. The samewas found to be true of the depth of the apodization, in term of numbersof layers.

The values for d=1/e were set to 5 for each end. The layers werenumbered in pairs, i.e. the layer number n=0 was used for each layer ofthe first ORU, n=1 for each layer of the 2nd ORU, n=2 for each layer ofthe 3rd ORU and so forth. In this manner each optical repeating unit hadan f-ratio of about 0.5. The alternative counting scheme wherein eachlayer receives a unique number n in the exponential formula was found tomake very little difference in the calculated spectra.

Although this example used an exponential tail distribution on the endsof a standard layer distribution, an apodization profile of one, two, ormore straight line or slightly curved line segments or other shapeswould also be effective for smoothing the spectral ringing. For example,a Gaussian distribution (1/e^2) would also suppress the spectralringing. We believe the main prerequisite is that a significant portionof layers of the apodizing profile have a significantly higher slopethan the baseline profile and are graded in the directions illustratedin FIG. 5. The average slope of the first 10 layers in the thin endapodizing profile 5 b of FIG. 5 is about 2.5 whereas the slope of thebaseline profile is about 0.2. These are different by a factor ofgreater than 10. The average slope of the first 6 layers is 16 timesthat of the baseline slope. An average slope of the first 10 layers thatis 5 times that of the average baseline slope (not shown) was also foundto significantly reduce spectral ringing.

Note that the bandwidth (at 90% of baseline reflection) was slightlyreduced by the apodization. This can be easily compensated, if desired,by a slight increase in the slope of the base profile which widens thefinal band.

Due to interference effects with the air/polymer surface reflections,laminates and protective boundary layers (PBLs) or skin layers can alsoplay an unexpectedly important role in the optical effects whichcontribute to spectral ringing. The spectral ringing is greater in theabsence of any optically thick layers or PBLs on the outer surfaces ofthe micro-layer stack. For example, note especially the pass axisspectra shown in FIG. 8, curve 8 b, which was modeled without anoptically thick layer or PBL on the outer surfaces of the partialreflector stack. An exception occurs though if the air interface isremoved by some anti-reflection technique or coating. For example, theringing at 60 degrees in air for p-polarized light (not shown) wouldthen be absent. 60 degrees is near the Brewster angle and the reflectionfrom the air/polymer interface is minimal near that angle.

For the wavelengths of these spectra, modeling showed that theapodization was most effective when the skins, PBLs, or any otherlaminates were about several micrometers thick or greater as illustratedin FIG. 8 curve 8 a. Additionally, modeling showed that if one side ofthe film stack had a PBL/skin layer and one did not, only the side withthe PBL/skin or other laminate had reduced spectral ringing.

Modeling showed that the amplitude and depth of the apodization profilecan both vary substantially and still provide a substantial reduction inringing. For example, the apodization amplitudes in this example were30% and 25% of the baseline layer thickness at opposite ends of thestack. These amplitudes were varied between 5% and 50% on either end andstill provided about the same reduction in ringing for a 1/e depth of7.5. Lesser amplitudes such as 5% or 10%, for example, were lesseffective, but still useful. The fractional amplitude A was taken to bethe fractional difference of the layer thickness at the end of astraight line fit to the baseline profile compared to the thickness atthe end (outer surface) of the apodizing profile.

Modeling showed that the 1/e depth of the profile can range from 3 to 10and be quite effective, but other values are still useful. To maximallyutilize the available number of layers, the depth should be kept to aminimum useful value. Modeling showed that only about 10 to 30 layers (5to 15 ORUs) were needed on each end of a 275 layer stack to provide abeneficial reduction in ringing. In general, it was found that,comparing film stacks with about the same reflectivity, more layers areneeded for both the baseline profile and the apodization profile whenthe index differential in the optical repeating unit is smaller. Theprofile shown in FIG. 5 was found to be near optimum for indexdifferentials of about 0.1.

Example 2 High Spectral Slope

Example 1 was for a modeled partial reflector having a substantiallyconstant reflectivity throughout the reflection band. Apodization isalso useful for stacks that produce a highly sloped spectrum. A baselinelayer profile (curve 9 a) having a substantially larger secondderivative than the profile in FIG. 5 is shown in FIG. 9, along with anapodizing profile (curve 9 b) on the thin end.

The spectra for the full baseline profile and the baseline withapodizing profile are shown as curves 10 a and 10 b respectively, inFIG. 10. The large spectral oscillation on the short wavelength end ofthe spectrum was significantly reduced with the apodizing profile curve9 b. Furthermore, with the apodizing profile, the overall spectrum wascloser to a triangular shape, with the high spectral slope continuing toshorter wavelengths.

Even though the baseline profile (curve 9 a) is substantially curved,the slope of the apodizing portion (curve 9 b) is still much larger thanthat of the baseline profile. The slope of the baseline where theapodizing profile joins the baseline is about 0.47 and the average slopeof the first 10 layers of the apodizing profile was about 3.37 which wasa factor of about 7 times greater. The average slope of the first 20layers of the apodizing profile was about 2.0 which was a factor ofabout 5 times greater. The average slope of the baseline profile isabout 0.3.

Intrinsic Bandwidth Considerations

The deviation of the apodizing layer thickness profile from the baselinelayer profile can also be expressed in terms of an optical coherencelength which is known as the intrinsic bandwidth (IBW). The intrinsicbandwidth is a measure of the strength of coherence of adjacent layersin terms of constructive interference leading to reflectivity.

A magnified view of the layer profile of FIG. 5 is shown in FIG. 11. Theintrinsic IBW of a stack is determined solely by the indices ofrefraction of the materials in the stack, and the IBW is given byIBW=4/π*Sin⁻¹[(n1−n2)/(n1+n2)], which is well known in the art of thinfilm reflectors.

For small index differentials this formula for IBW can be simplified tofirst order asIBW=4/π*[(n1−n2)/(n1+n2)].

More generally for any polarization or angle of incidence:IBW=4/π*r,where r is the Fresnel reflection coefficient for the interface betweenthe material layer pairs. The expression [(n1−n2)/(n1+n2)] isrecognizable as the value of r for light at normal incidence on a stackof alternating layers of index n1 and n2 where n1>n2.

The IBW is a fractional bandwidth Δλ/λo whereIBW=Δλ/λ₀=4/π*r.

Since layer thickness is directly proportional to the center wavelengthof reflection via the familiar relationship between wavelength λ andlayer thickness d at normal incidence: ¼λ=nd, we can also write:Δd/d ₀=IBW or Δd/d ₀=4/π*r

In this manner one can determine the approximate range of contiguouslayers in a graded stack which are working in a substantially coherentmanner to reflect a given wavelength λ₀ which is associated with a layerof thickness do. For a film stack with a monotonically increasing ordecreasing layer profile, the layers that are strongly coupled to anygiven layers are those on both sides of that layer within a thicknessrange of +/−Δd, where Δd is given by the above formula.

Thus the range of 2*Δd can be used to determine ΔN, the number of nearbylayers that work in a coherent fashion for substantial reflectivity,when the layer profile is known. ΔN can be determined only if the layerprofile is given, as ΔN depends on the slope of the layer thicknessprofile. The reflectivity of a stack at a certain wavelength λ=4n*d₀,where d₀ is the thickness of a layer in the stack, can be shown to beproportional to the local slope of the layer profile, and is givenapproximately by the following formula, where r, ΔN, and IBW aredetermined as described above. More precisely, do is half of the opticalrepeat unit of a quarterwave stack.

$T = {{Exp}\left\lbrack \frac{{- r^{2}}*\Delta\; N*a*d_{0}}{\Delta\; d} \right\rbrack}$

The value of the factor “a” is an adjustable parameter. A value of a=2gives appropriate values for the reflectivity. In simple cases, theratio ΔN/Δd is 1/slope of the layer thickness profile. However, if theslope is zero, or the layer profile has short term reversals of sign inthe slope, or if the layer is near the beginning or the end of thestack, the ratio ΔN/Δd must be determined by the graphical techniqueoutlined below in association with FIG. 11. Ad is then given by theformula Δd=2*IBW*d₀, and ΔN is all of the contiguous layers that arewithin a distance of this Δd on both sides of the chosen layer ofthickness d₀. This formula is intended as a guide to determine theapproximate reflectivity of stacks that have a smooth and continuouslayer profile. It will not work for all cases, such as stacks with largepositive and negative variations in layer thicknesses between adjacentlayers or layer pairs. Also note that it does not include the reflectiveinterface between the stack and air, or other layers laminated to thestack.

For the example profile in FIG. 11, assuming the low and high indexlayers are 1.564 (PETg) and 1.675 (partially oriented coPEN of Example1), the IBW is 0.0436, or 4.36%. Twice that value is 0.0872. The rangeof coherent reflection on either side of a given layer of thickness dois for layers that are +/−4.36% thicker or thinner than d₀. Note that inthe baseline section of the stack, this translates to about 34 layers.In the highly sloped region of the apodization section, only 2 to 4layers provide constructive interference in a substantially coherentfashion.

The magnitude of the deviation of the apodizing profile from that of thebaseline profile can be expressed in terms of the IBW. This is usefulsince the IBW is related to the index differential in the optical repeatunit of the stack. In general, the fractional amplitude A of theapodizing profile can be in the range of 3 to 10 IBWs or even greater.The amplitude of the apodizing profile in FIG. 11 is about 7 IBWs.

In order to produce a broadband reflector with controlled color, a layerprofile can be monotonically increasing or decreasing in thickness, withminimal disruptions. The monotonic restriction applies to all layers ofthickness that apply to the broadband wavelength range of interest.Layer thickness anomalies should be on the order of +/−1 IBW in order tocreate a smoothly varying spectrum.

Monotonically Varying Layer Thickness of an Optical Repeating Unit Alonga Multilayer Film.

The thickness of the optical repeating unit shows a consistent trend ofincreasing along the thickness of the multilayer film (e.g., thethickness of the optical repeating unit does not show an increasingtrend along part of the thickness of the multilayer film and adecreasing trend along another part of the multilayer film thickness).These trends are independent of layer-to-layer thickness errors, whichmay have a statistical variance with a 1-sigma value as large as 2% ormore. In addition, a local disruption in the optical repeating unitthickness, such as those that can be noted in FIGS. 12, 14 and 16 maynot be strictly monotonic by the mathematical definition, but themagnitude of the local deviations of layer thickness from a monotonicand smoothly varying layer profile should be kept to a minimum.

The intrinsic bandwidth relationship provides insight into the necessarylimits of local disruptions in the layer profile and to requiredmagnitude of the apodization profile. A localized layer profiledisruption in the interior of the profile that is greater than about+/−1 IBW can cause a rather significant oscillation in the spectrum ofthe stack. Such local thickness deviations are preferably less thanabout +/−0.5*IBW, or less than +/−0.25*IBW.

Alternative Apodizing Profiles

The exponential deviation from the baseline profile provides a goodapodization for a broadband stack. The exponential profile has acontinuously changing slope and the derivative of the slope is also anexponential. Other profiles are also effective. In general, anycontinuous and quickly changing slope near the end of a baselineprofile, provides the desired reduction in spectral ringing. The firstderivative, or slope, of the apodization layer profile at the end layeris desirably much higher, on the order of 5, 7 or 10 times higher, thanthe slope of the baseline profile where the apodization profile joinsthe baseline profile. The number of layers in one apodization profilecan be about 3%, 5%, 10% or 15% of the total number of layers in thestack, where the stack is composed of a continuous profile of opticalrepeating units and is generally increasing in thickness from one end toanother. Small deviations of some layers from this ideal profile can betolerated, but local deviations of more than one intrinsic bandwidth,with both positive and negative slopes, can cause significantdisruptions of the spectral response at localized wavelengths.

The average slope of the apodization layer profile, measured from theend layer to a layer whose number is 5% of the total number of layers,can be about 4 or 5 times higher than the average slope of the baselineprofile and give effective spectral smoothing.

Example 3 Polymeric Apodized on the Red Spectral Side

Using the feedblock method described in U.S. Pat. No. 6,783,349, a 275microlayer packet of alternating low and high index polymer layers wascoextruded as a cast web and then oriented with a constrained uniaxialstretch of about 6:1 in a standard film tenter. The high indexbirefringent material was a 90/10 coPEN (90% naphthalate units to 10%teraphthalate units).

The stretching temperatures and rates were adjusted so as to obtain thefollowing set of indices for the birefringent high index 90/10 coPENpolymer: nx≈1.82, ny≈1.62, nz≈1.50, where x is the transversetenter-stretched direction. The low index material was NEOSTAR FN007copolyester ether elastomer, available from Eastman Chemical (Kingport,Tenn.), which has an index of about 1.505. All indices were measured at633 nm.

The layer thickness profile of the 275 microlayers of the oriented filmwas measured using Atomic Force Microscopy (AFM), and is shown in FIG.12. After orientation, a 100 micrometer thick film of clear PET waslaminated to the thick layer side of the film stack using a 50micrometer thick layer of clear pressure sensitive adhesive. The filmwas so laminated to suppress extraneous spectral ringing which can becaused by interference of light reflected from the front and backair/polymer interfaces of the film. The resulting spectrum for they-axis of the film, measured at normal incidence with light polarizedparallel to the y-axis of the film is shown in FIG. 13.

Layer profile FIG. 12 included an apodizing profile on the thick end ofthe stack. The average slope of the baseline profile was about 0.37. Theaverage slope for the outer 10 layers of the apodizing profile was about4.3, the average slope for the last 14 layers was about 3.3 and theaverage slope for the last 20 layers was about 2.3. When divided by theslope of the baseline profile, these yield ratios of about 12, 9 and 6respectively. The equation for the straight line fit of the base profilewas t=0.3728*n+62.41. At the maximum value of n=275, the baselinethickness value was 165 nm. Layer number 275 was measured to be 214 nmthick. The fractional amplitude difference A was given byA=(214−165)/165≈0.3. The apodizing profile joined the baseline profilenear layer number 240. Thus about 13% of the layers were utilized forthe apodization profile.

The difference in the blue and red ends of the spectrum are readilyapparent in FIG. 13. The large oscillations in the transmission spectrumin the blue were absent at the long wavelength end of the spectrum dueto the use of the apodizing layer profile. The overall shape of thespectrum could be changed, if desired, by adjusting the shape of thebaseline layer profile as illustrated by Example 2.

Example 4 Polymeric Apodized on the Blue Spectral Side

Using the feedblock method described in U.S. Patent Application61/332,401 (3M Docket No. 64248US002) filed May 7, 2010, two 275 layerpackets of alternating low and high index polymer layers were coextrudedas one cast web and then stretched in a sequential biaxial orientationfilm line. The multilayer cast web was first stretched with a stretchratio of about 3.5 to 1 in a length orienter and then transverselystretched in a tenter with a stretch ratio of about 6.5 to 1. Thestretching temperatures were adjusted so as to obtain the following setof indices for the film: the high index layers were PEN homopolymer withnx≈1.80, ny≈1.70, nz≈1.48, where x is the more highly stretchedtransverse direction, and the low index material was a blend of 27%90/10 coPEN and 73% PETg, the blend having index n≈1.584 for x, y, and zdirections and showing minimal birefringence compared to the PEN layer.

After stretching, the two packets of layers were peeled apart along theinterior PBLs of each stack. The two PBLs were the same material, andthus merged into one layer which in this case adhered to the thick layerside of packet #1 during the peeling process. Packet #1 was used forthis example and had a skin layer of about 15 micrometers on the thinlayer side and a PBL of about 5 micrometers thickness on the thick layerside.

The layer profile of the 275 microlayers of the oriented film packet wasmeasured using Atomic Force Microscopy (AFM), and the layer thicknessprofile is shown in FIG. 14. In this example, an apodizing layer profilewas applied to the thin layer end of the film stack.

The average slope of the baseline profile was about 0.43. The averageslope for the first 10 layers of the stack was about 3.4, for the first14 layers about 2.5 and the average slope for the first 20 layers wasabout 1.75. These yielded ratios of about 8, 6, and 4, respectivelycompared to the average baseline slope. The equation for the straightline fit of the base profile was t=0.427*n+64.623. The thinnest layer ofthe apodizing profile (layer #1 of the stack) was 35 nm. The fractionalamplitude A of the apodizing layer profile was≈(65−35)/65=0.46.

After peeling the two film packets apart, a 100 micrometer thick film ofclear PET was laminated to the thick layer side of packet #1 using a 50micrometer thick layer of clear pressure sensitive adhesive. On the thinlayer side of this stack, a 50 micrometer thick layer of clear pressuresensitive adhesive was applied. The resulting spectrum for the pass axisof this polarizing film, measured at normal incidence with lightpolarized parallel to the y-axis of the film, is shown in FIG. 15.

As expected from the modeling efforts, the ringing was substantiallyeliminated on the blue end of this spectrum but substantial spectraloscillations were present on the red end. The effect of the laminate onthe thick layer side was mainly only a smoothing of the finer ripplescaused by interference from the two air interfaces on the film. The AFMlayer profile showed an increase in slope for several layers on the redend, but the profile was not deep enough nor of high enough amplitude toeffectively reduce the spectral oscillation on the red end. By contrast,the spectral ringing is effectively eliminated on the thin layer side

Example 5 Polymeric Film Apodized on the Blue Spectral Side

Using the feedblock method described in U.S. Patent Application61/332,401 (3M Docket No. 64248US002) filed May 7, 2010, two 275 layerpackets of alternating low and high index polymer layers were coextrudedas cast web and then stretched in a sequential biaxial orientation filmline. The multilayer cast web was first stretched with a stretch ratioof about 3.5 to 1 in a length orienter and then transversely stretchedin a tenter with a stretch ratio of about 6.5 to 1. The stretchingtemperatures were adjusted so as to obtain the following set of indicesfor the film: the high index layers were PEN homopolymer with nx≈1.80,ny≈1.70, nz≈1.48, where x is the more highly stretched transversedirection, and the low index material was a blend of 27% 90/10 coPEN and73% PETg, the blend having index n≈1.584 for x, y, and z directions andshowing minimal birefringence compared to the PEN layer.

After orientation, the two packets of layers were peeled apart along theinterior PBLs of each stack. The two PBLs were the same material, andthus merged into one layer, which in this case adhered to the thicklayer side of packet #1 during the peeling process. packet #2 was usedfor this Example and thus had no PBL or skin layer on the thin layerside. A layer of optically clear tape was applied to the thin layer sideof packet #2 and the spectrum was measured on this laminate at normalincidence, for light polarized parallel to the y axis, and was plottedin FIG. 17. The thick layer side of this packet was in contact with thecoextruded skin/PBL which was about 10 micrometers thick. The layerprofile of the 275 microlayers of the oriented film packet was measuredusing Atomic Force Microscopy (AFM), and the layer thickness profile isshown in FIG. 16. In this example, an apodizing layer profile wasapplied to the thin layer end of the film stack.

The average slope of the baseline profile was about 0.37. The averageslope for the first 10 layers of the stack was about 4.1, the averageslope for the first 14 layers was about 3.0 and for the first 20 layerswas about 2.1. These layer numbers represented 3.6%, 5.1% and 7.3% ofthe total layers in the stack, respectively. These numbers also yieldratios of about 11, 8, and 6, respectively, when compared to the averagebaseline slope. The equation for the straight line fit of the baseprofile was t=0.3747*n+75.598. The thinnest layer of the apodizingprofile (layer #1 of the stack) was≈40 nm. The fractional amplitude A ofthe apodizing layer profile was≈(76−40)/76≈0.47.

As expected from the modeling efforts, the ringing was substantiallyeliminated on the blue end of this spectrum but substantial spectraloscillations were present on the red end. The effect of the laminate onthe thick layer side was mainly only a smoothing of the finer ripplescaused by interference from the two air interfaces on the film. The AFMlayer profile showed an increase in slope for several layers on the redend, but the profile was not deep enough nor of high enough amplitude toeffectively reduce the spectral oscillation on the red end. By contrast,the spectral ringing was effectively eliminated on the thin layer side.

The average slope for the last 10 layers on the thick layer side wasabout 0.86, the average slope for the last 14 layers was about 0.80, andthe average slope for the last 20 layers was about 0.68. These valuesyielded low ratio values of 2.32, 2.16 and 1.84, when compared to theaverage baseline slope. Layer number 275 was measured to be 187 nmthick. Using the equation for the straight line fit (t=0.3747*n+75.598)with n=275 the baseline thickness was about 179 nm at layer 275. Thefractional amplitude difference A was by A=(187−179)/179≈0.045.

In general, the apodization technique describe above is very effectivein eliminating the phenomenon of in-band spectral ringing (oscillationof the transmission spectrum). Improvements in extrusion equipment canprovide for overall improvements in the shape of the spectraltransmission curve by reducing the short term variations in the layerprofiles that are evident in FIGS. 12, 14 and 16.

In other embodiments, apodized stacks are useful in cases where two ormore partially reflective stacks are combined to increase thereflectivity in part or all of the wavelength range of the one of thestacks without introducing substantial disruptions in the spectrum ofthe combined stack. Such combined film stacks without apodization aredescribed in PCT filed application US2011/035967 entitled “PartiallyReflecting Multilayer Optical Films With Reduced Color.” The film stacksdescribed therein can benefit from the use of apodizing profiles oneither the thin end or on the thick end or on both ends of each packet.

The apodizing profiles described herein are intended for broadbandreflectors that are constructed with a graded layer thickness baselineprofile and exhibit in-band ripple. Instead of a graded thicknessapodizing profile, the apodizing function can also be achieved with agraded index profile on the ends of the baseline layer thicknessprofile. With a graded index profile, the ORU thickness values do notnecessarily deviate from the baseline profile: the index difference Δnsimply approaches zero on the end of the stack. The gradation of Δn canfollow an exponential profile or other profile similar to the onesdescribed above for thickness graded apodizing profiles. The gradedindex profile can be real or virtual. An example of a virtual gradedindex is a gradation of the f-ratio of the stack throughout the ORUs ofthe apodizing profile. Combinations of graded index and graded layerthickness profiles can also be used as apodizing profiles.

Thus, embodiments of APODIZED BROADBAND PARTIAL REFLECTORS aredisclosed. One skilled in the art will appreciate that the optical filmsand film articles described herein can be practiced with embodimentsother than those disclosed. The disclosed embodiments are presented forpurposes of illustration and not limitation.

What is claimed is:
 1. A broadband partial reflector comprising: amultilayer polymeric optical film having a total number of opticalrepeating units that monotonically increases in thickness value from afirst side to a second side of the multilayer polymeric optical film,wherein the multilayer polymeric optical film is designed to reflectlight at visible, infrared, or ultraviolet wavelengths, the multilayerpolymeric optical film having: a baseline optical repeating unitthickness profile defined by a first plurality of optical repeatingunits and having a first average slope; and a first apodized thicknessprofile of the multilayer polymeric optical film defined by a secondplurality of optical repeating units and having a second average slopebeing at least 5 times greater than the first average slope, wherein thesecond plurality of optical repeating units define the first side of themultilayer polymeric optical film and join the first plurality ofoptical repeating units, the second plurality of optical repeating unitsare in a range from 3-15% of the total number of optical repeatingunits, and wherein the first apodized thickness profile has a firstlayer thickness that is at least 15% thinner than any of the firstplurality of optical repeating units.
 2. A broadband partial reflectoraccording to claim 1, wherein the second plurality of optical repeatingunits increase in thickness in a range from 1.1× to 2×.
 3. A broadbandpartial reflector according to claim 1, wherein the total number ofoptical repeating units is in a range from 50 to
 1000. 4. A broadbandpartial reflector according to claim 1, wherein the second average slopeis at least 10 times greater than the first average slope.
 5. Abroadband partial reflector according to claim 1, wherein the firstapodized thickness profile exponentially deviates from the baselineoptical repeating unit thickness profile.
 6. A broadband partialreflector according to claim 1, wherein the polymeric multilayer opticalfilm is designed to reflect light at ultraviolet wavelengths.
 7. Abroadband partial reflector according to claim 1, wherein the firstapodized thickness profile has a first layer thickness that is at least25% thinner than any of the first plurality of optical repeating units.8. A broadband partial reflector according to claim 1, wherein thebroadband partial reflector reflects 10-90% of visible or IR light overa range of at least 100 nm for light polarized parallel to one opticalaxis.
 9. A broadband partial reflector according to claim 1, furthercomprising an optically thick layer optically coupled to the first side,wherein the optically thick layer is at least 10× thicker than at leastone of the first plurality of optical repeating units.
 10. A broadbandpartial reflector according to claim 1, further comprising ananti-reflection layer disposed on the first side.
 11. A backlight,comprising the broadband partial reflector according to claim
 1. 12. Aliquid crystal display, comprising the broadband partial reflectoraccording to claim
 1. 13. A luminaire, comprising the broadband partialreflector according to claim 1.